Abstract
This paper presents a comprehensive analytical method to solve the fourth-order differential equation relevant to bending analysis of bi-directional functionally graded (BDFG) nanobeams obtained by the Eringen's nonlocal elasticity theory. Unlike usual numerical solutions (e.g., by following the Differential Quadrature method), analytical solutions following the Laplace transform are adopted. The material properties of the nanobeam vary along both the thickness and the axial directions by following the power law and the exponential law, respectively. Explicit equations are presented for bending displacements of BDFG nanobeams under various distributions of applied loads in combination with a few common boundary conditions. The effects of material inhomogeneity parameters along both the axial and the thickness directions, as well as that of the nonlocal parameter, are investigated. Comparisons with a few available results in the literature demonstrate the accuracy and unravel the versatility of the presented analytical method.
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